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If you want a bottle of ketchup to erupt, just add warmth. It doesn't even take that much. (just hold it in your crotch for a while) Combine that with an air bubble and ketchup up by the cap, and you've got good times. The take-away: heat + tomato product = excessive gaseous expansion

Second bit - order a glass of beverage and a straw. (glass glass is most effective) Using your mouth and woodwind instrument playing skills ideally, blow a quick/hard/small "DHU!" of air into the bottom of the cup. You will see the liquid lurch upward, and if you have the chops, the entire cup will hop upward and slam back down into the table. The take-home: rapid gas expansion at the bottom of a big glass of beverage causes the cup to jump.

The rest, I leave up to you all. Knowing is half the battle!

edit: I've always wanted to know why blowing into a glass of water in that fashion makes it hop so. It doesn't totally make sense in my brain, so I find watching/hearing it very entertaining.

edit edit: the sticking is just probably metal NOT-BOILING-HOT microwave ceiling cooling enough steam enough to stick. For the record. And if I have to, I'll record some video demonstrations tomorrow at work.

for your second bit: the glass probably moves upward as a way to fill the low-pressure bubble that you created, since the liquid isn't filling it fast enough (because it is too busy moving upward first from the force of the bubble)

4 doesn't sound right. The momentum of the liquid can't make the glass move up. But if the liquid moving upwards creates low enough pressure in the bottom of the glass, it would suck the glass up. If the force due to pressure imbalance was enough to overcome gravity.

I don't think that the cup would move up to fill a low pressure system, that would take far more energy than just pulling liquid into the space. I think that the cup rising off the surface may be due to a combination of forces.
1 - Inertia from the gas being pushed into the glass may result in a rebound off the table.
2 - The rapid rise of the air bubble is raising the water, which due to friction also exerts an upward force on the glass (sides).

I thought that the ketchup burst because of vinegar separating from water. Otherwise, what else about tomato juice could cause this? To observe the phenomenon, just boil V8 on the stove. But don't ask me to clean it up.

there was some liquid underneath the bottom of the cup. As the microwave operated, that liquid became superheated (above boiling point but still in liquid state). Then at some point, something caused a small cavitation (perhaps the friction of the turntable stopping when the microwave timer finished) and the thin, uniform layer of superheated liquid all boiled at once, providing considerable and relatively even force pushing the cup upwards.

Then since the microwave cycle had finished, the juice in the cup was no longer boiling and as it started to cool, the juice vapor in the top area of the cup was shrinking in volume as it cooled and condensed.

Because these two things happened at exactly the same time, the cup got shot up to the ceiling of the microwave and stuck there due to the slight vacuum now formed by the juice steam re-condensing.

//edit:

As suggested by tyroney, GinsuGuy, Zippytiewassabi and others, perhaps the launching effect occurred inside the glass rather than underneath it. Give them some love.

If some of the liquid near the bottom of the glass became superheated, then flash-boiled it would quickly be cooled by the rest of the non-superheated juice in the glass. This would spray juice everywhere, and account for the nearly perfectly circular splash pattern on the microwave roof.

As the flash-boiled juice rapidly cooled below the boiling point, that could create a noticable vacuum against the bottom of the glass which could pull the glass up. Then it hits the roof, juice keeps cooling, so it stays there.

I propose that when the glass hit the ceiling of the microwave, it sloshed the V8 which caused the hotter air and exterior of the liquid to mix with the cooler interior just enough to cause the air to cool into slightly vacuumed state. You turning off the machine aided the vacuum. You could have turned on the microwave to heat it up and reduce the vacuum force.

I'm not a physicist, but I've been sitting here staring at the image while scratching myself in order to keep from having to go to bed.

My only issue with your theory is that the forces involved seem too small, and they don't seem to explain the messiness and splatter patterns inside the microwave. Specifically, I don't think that the rapid vaporization of ~0.5 mL of V8 would be enough to propel ~1 lb several inches into the air. And if the cavitation was caused by a horizontal dislodging force, then I would expect the cavitation to be asymmetrical, causing an inhomogeneous boiling event and causing the cup to tip at least somewhat, ruining the formation of the final seal. I don't think that cooling is enough to explain the adhesion of ~1 lb of liquid and glass (not an ideal material in this case) to the top of the microwave interior. The cooling would be much too slow, I think an instantaneous decrease from 373 K (boiling) to 298 K (room temp) would cause the gas pressure to decrease by ~20% - I don't know if that would be enough of a differential to cause the suction, but it definitely wouldn't cool down that fast.

I get the impression, after staring at it, that the V8 exploded from the cup while it was sitting at the bottom. The weird thing that happened in this case (I hypothesize) is that the liquid, perhaps through relatively high viscosity, essentially formed a column of liquid from the cup all the way to the top of the microwave interior. The simultaneous boiling and displacement of gas from above the cup would have created a fairly high gas pressure in a short time window, filling the microwave and causing the "bang" sound described by the OP. Simultaneously, the cup was lightened by removing its load of V8. Perhaps there was a low vacuum inside the cup from the upward explosion of the liquid? The two effects - the increased density of the medium (heated and compressed gas + V8) and the decreased density of the glass caused the cup to rapidly "float" toward the top of the microwave. The liquid column hit the top of the microwave interior at high velocity, causing the sharply outlined spill. Most of it fell back into the cup (causing the surprisingly small lossage evident in the picture), but the amount which was outside of the cup brim fell to the bottom, some of it bouncing back up to the sides as a type of ricochet. As the cup came close to the top of the microwave interior, the liquid, the top of the microwave interior, and the cup formed a closed system with a relatively small amount of gas trapped inside. If the volume of liquid which fell into the cup plus the volume of gas present in the column is less than the volume of the cup, then the gas will have to expand to fill the necessary volume and hey presto you've got a pressure differential, finalizing the cup's adherence to the top of the microwave interior. Any cooling of the system would be icing on the cake, strengthening the adherence of the cup to the microwave.

Either way, this is one in a million and something weird and somewhat nonsensical had to happen. Who knows, maybe this all made up. Whatever. I'm going to bed now.

Nah, you can easily do it with tap water, as long as you don't have particulate. Dissolved stuff is no problem. It's pretty insane that he managed to get this effect in a microwave, though. He must be using lens wipes on that sucker.

Not necessarily. I work in a lab and I often melt a sugary powder like substance ( agarose ) in a buffer which itself is water with a number of other chemicals dissolved in it ( TAE ), and it often gets super heated. After a minute or so in the microwave I will open the door and it's not boiling, but as soon as I agitate the glass flask it will bubble/boil for a few seconds. In this case the microwave doesn't rotate so it's perfectly still as it heats, and then I guess the movement causes it to boil.

first, agarose is NOT a "sugary powder like substance" more like little balls of gelatin. You are undoubtedly running a DNA gel and using milli-Q water, which is ultrapure. The key to superheating is to not have a nucleation site, and it has to be homogenous, so the chemicals (tris acetic acid and EDTA) in your buffer are not going to interfere with the process. Also, laboratory vessels usually are ultra smooth compared to housewares, again making it easier to superheat.

FYI, this also happens in microwaves that rotate. I'm thinking it has something to do with the agarose at the bottom of the flask. Perhaps you're superheating a layer and the aeration from swirling makes the liquid boil over.

That is an interesting theory, however, I don't account for thin layer of boiling liquid underneath the cup for have enough force to move it that far. I've seen containers of soups to literally jump while in the microwave. From some of the research I have done, it is a reaction internal to the cup that caused it to jump. Check the glass/cup manufacturer to make sure it is microwave save, there could be a material/metal used in it's manufacturing that causes a charge build-up and arcing. This arcing can cause short, intense moments of kinetic energy (campbell's soup bowls are notorious for this, as they have a small metallic ring on them).

I think the liquid inside the cup at the bottom became superheated. It instantly flashes into steam, pushing the liquid above it upward. The steam quickly stops expanding and forms a partial vacuum, momentum of the liquid carries the cup upward. A hermetic seal forms as the glass reaches the top of the microwave. The agitation/aeration causes a loss of temperature adhering the glass.

'...and Lo! the water was truly turned to wine. And the guests said unto Jesus "Awesome! Do another one!" And Jesus levitated a hot carbonised vegetable beverage, wherupon the guests did congatulate him hertily, saying unto Him "Woo!" and "Yeah!". Shortly thereafter young child came to Jesus saying "Meh. Bet you can't change Coke to Pepsi" and Jesus was humbled for it was so.' - Ezekiel 13:37

You guys should try putting Spicy V8 on (hot) pasta—preferably shells because they act like little cups. It's really good actually and one of the little cans is the perfect amount of sauce for one bowl. It was one of my college staples.

so what, it's basically just tomato juice. Guess what. Orange juice tastes like oranges. Apple juice tastes like apples. And V8 tastes like tomatoes. Personally I love V8 now and then. I have no idea why they don't just admit it's tomato juice.

I wonder if the metal cans have anything to do with it? My microwave was freaking out recently, popping blue sparks and such, then I realized there was a beer bottle cap underneath that was causing it. Acted normally again when I took it away.

I made this joke to my girlfriend and she got mad at me for speaking nonsense. She had apparently never heard the bit and when I tried to introduce her to it, two minutes in she was madder at me than before when I had made the joke...

"If you've tried to use one of Aperture's microwaves during your visit, you may have noticed a strange effect, especially if your food contains tomatoes, potatoes, or avocado. Well, it seems that one of our interns mislabelled the anti-grav generators as microwave parts. Good news is, they'll still warm your food. Bad news is, your food might contain life-threatening levels of radiation. We haven't confirmed that yet, though, so it's up to you if you want to risk it. Depends on how hungry you are, really."

Here is my guess: The bottom of the cup created a suction cup because it was wet. After being heated for a while, the bubble at the bottom exploded and made the cup go to the top. Then the top created a suction cup because it cooled down at the top.

Here is my guess: The bottom of the cup created a suction cup because it was wet. After being heated for a while, the bubble at the bottom exploded and made the cup go to the top. Then the top created a suction cup because it cooled down at the top. MAGIC

There were probably no nucleation sites in the cup and the V8 became super heated. It finally boiled up in one huge bubble and all the V8 shot out of the glass. This did two things. It created enough force to make the glass shoot up to the top, and also reduced the temperature of the glass. When the rapidly cooling glass hit the top, it created a vacuum. And that's what probably happened.

My educated guess is that an air bubble formed inside of the very thick V8. When it popped the glass shot into the air. Somehow the glass formed an airtight seal with the roof of the microwave, and the cavity formed by the bubble closed, forming a suction-cup type bond.

Okay. The particle accelerator in the top of the microwave generates alternating positive and negative charges to molecules of air inside the microwave, heating them up. This same phenomenon is also transmitted directly to whatever is in the microwave.

When glass is placed in a microwave, its net charge stays roughly neutral because a microwave's dielectric emitter just isn't good at heating up anything that thoroughly solid or resistant to heat transfer, but the microwave still tries to shift it from negative to positive with little results unless the glass has something in it to heat up--in which case the glass feels hot because of its contents.

Now, placing metal (cans) on top of the microwave does this: it absorbs and attracts positively-charged dielectric emissions from the microwave, giving the cans a highly positive net charge while ALSO giving the glass inside the microwave a very NEGATIVE charge because that's the only dielectric emission making its way to the glass. The cans become positively charged and the glass negatively charged, but they remain this way as long as the microwave is on and will not shock you if you touch them because there is an electric link established between the cans and the glass. I wouldn't be surprised if you saw a few flashes of electricity when you were heating up the glass.

Now I don't know how strong the charge could get, but if something caused the polarized charges in each the glass and cans to suddenly spike, the glass could conceivably have been magnetically attracted to the cans and slammed into the microwave's ceiling.

V8 is thixotropic. When you heated the V8, the portion in the bottom boiled, creating an explosive air bubble. This bubble pushed the heated and thin material above it upward and the glass downward. The microwave plate acted like a trampoline, and the cooling V8, launched upward by the bubble cooled, and became thick enough again to pull the glass upward with it. The thin V8 splashed on the ceiling also thickened to the point where it sealed the glass against the ceiling. As the rest of the V8 cooled, it formed a vacuum, making it difficult to remove the glass. This would not have happened had the material not been thixotropic.

I've seen this. The cup was touching the top of the microwave when the microwave started. Contents heat up and overflow as they get hotter, but the expanding gas is less dense than it was when it was cool. After the ding, the contents cool creating a vacuum in the glass that adheres it to the top of the microwave. Whatever object that pressed the glass up against the top is removed and probably thrown away.
Elementry.

I don't know how this could have happened the way OP says it did, but I know how I would do it if I wanted to take a picture for the internet, use a cardboard stand or something to press the glass against the ceiling, run it for about a minute, let cool, then take out the stand and you'll have a glass vacuum sealed to the ceiling.

OK, here is an idea, recreate the scenario again, as closely as possible to the first incident, record the event and post it so that we may observe. We have all formed observed the data thus far and formed hypotheses, now lets perform another step of the scientific method and experiment.

My theory is that a huge v8 bubble (probably comprised of smaller bubbles), bubbled over and filled space all the way to the very top wall of the microwave (looks like the glass was full to the brim). Then, somehow, when it popped it created a vacuum.

I'm mostly posting this so I remember to come back here for the real answer. Come on engineers, explain this shit.